Let X be a standard normal distribution. The value of E (X³) is:

Question

Question

This question was previously asked in

SSC CGL Tier-II ( JSO ) 2019 Official Paper ( Held On : 17 Nov 2020 )

Answer 1

Explanation

The probability distribution function of Normal distribution us was given as

⇒ F(x) =[1/σ√2π ]e^{-(x – μ)2/2σ2}

If we put Z = (x – μ)/σ in Normal distribution then it is called a standard normal distribution

The probability distribution function of the standard normal distribution is as follows

⇒ f(x) = [1/σ√2π]e^{- z^2/2}

The value of E(X³) in a standard normal distribution is 0

The standard deviation of normal distribution = σ = 1

The coefficient of skewness of Normal distribution is β₁ = 0

The coefficient of kurtosis in normal distribution is β₃ = 3